Multi-layered tensor networks for image classification

TL;DR

This paper introduces a multi-layered tensor network model for image classification that reduces computational costs while maintaining performance by performing a single MPS operation per layer and preserving spatial correlations.

Contribution

It proposes a non-patch based multi-layered tensor network (MLTN) that simplifies the architecture and improves efficiency over previous patch-based models like LoTeNet.

Findings

MLTN reduces computation cost compared to LoTeNet.

MLTN maintains classification performance despite architectural simplification.

MLTN effectively learns linear decision boundaries in high-dimensional spaces.

Abstract

The recently introduced locally orderless tensor network (LoTeNet) for supervised image classification uses matrix product state (MPS) operations on grids of transformed image patches. The resulting patch representations are combined back together into the image space and aggregated hierarchically using multiple MPS blocks per layer to obtain the final decision rules. In this work, we propose a non-patch based modification to LoTeNet that performs one MPS operation per layer, instead of several patch-level operations. The spatial information in the input images to MPS blocks at each layer is squeezed into the feature dimension, similar to LoTeNet, to maximise retained spatial correlation between pixels when images are flattened into 1D vectors. The proposed multi-layered tensor network (MLTN) is capable of learning linear decision boundaries in high dimensional spaces in a multi-layered setting, which results in a reduction in the computation cost compared to LoTeNet without any degradation in performance.